409 lines
200 KiB
Plaintext
Vendored
409 lines
200 KiB
Plaintext
Vendored
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Tutorial: One dimensional Helmholtz equation using Periodic Boundary Conditions\n",
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"\n",
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"[](https://colab.research.google.com/github/mathLab/PINA/blob/master/tutorials/tutorial9/tutorial.ipynb)\n",
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"\n",
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"This tutorial presents how to solve with Physics-Informed Neural Networks (PINNs)\n",
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"a one dimensional Helmholtz equation with periodic boundary conditions (PBC).\n",
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"We will train with standard PINN's training by augmenting the input with\n",
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"periodic expansion as presented in [*An expert’s guide to training\n",
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"physics-informed neural networks*](\n",
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"https://arxiv.org/abs/2308.08468).\n",
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"\n",
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"First of all, some useful imports."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {},
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"outputs": [],
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"source": [
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"## routine needed to run the notebook on Google Colab\n",
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"try:\n",
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" import google.colab\n",
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"\n",
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" IN_COLAB = True\n",
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"except:\n",
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" IN_COLAB = False\n",
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"if IN_COLAB:\n",
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" !pip install \"pina-mathlab\"\n",
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"\n",
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"import torch\n",
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"import matplotlib.pyplot as plt\n",
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"import warnings\n",
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"\n",
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"from pina import Condition, Trainer\n",
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"from pina.problem import SpatialProblem\n",
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"from pina.operator import laplacian\n",
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"from pina.model import FeedForward\n",
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"from pina.model.block import PeriodicBoundaryEmbedding # The PBC module\n",
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"from pina.solver import PINN\n",
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"from pina.domain import CartesianDomain\n",
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"from pina.equation import Equation\n",
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"from pina.callback import MetricTracker\n",
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"\n",
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"warnings.filterwarnings(\"ignore\")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## The problem definition\n",
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"\n",
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"The one-dimensional Helmholtz problem is mathematically written as:\n",
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"$$\n",
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"\\begin{cases}\n",
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"\\frac{d^2}{dx^2}u(x) - \\lambda u(x) -f(x) &= 0 \\quad x\\in(0,2)\\\\\n",
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"u^{(m)}(x=0) - u^{(m)}(x=2) &= 0 \\quad m\\in[0, 1, \\cdots]\\\\\n",
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"\\end{cases}\n",
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"$$\n",
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"In this case we are asking the solution to be $C^{\\infty}$ periodic with\n",
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"period $2$, on the infinite domain $x\\in(-\\infty, \\infty)$. Notice that the\n",
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"classical PINN would need infinite conditions to evaluate the PBC loss function,\n",
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"one for each derivative, which is of course infeasible... \n",
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"A possible solution, diverging from the original PINN formulation,\n",
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"is to use *coordinates augmentation*. In coordinates augmentation you seek for\n",
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"a coordinates transformation $v$ such that $x\\rightarrow v(x)$ such that\n",
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"the periodicity condition $ u^{(m)}(x=0) - u^{(m)}(x=2) = 0 \\quad m\\in[0, 1, \\cdots] $ is\n",
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"satisfied.\n",
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"\n",
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"For demonstration purposes, the problem specifics are $\\lambda=-10\\pi^2$,\n",
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"and $f(x)=-6\\pi^2\\sin(3\\pi x)\\cos(\\pi x)$ which give a solution that can be\n",
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"computed analytically $u(x) = \\sin(\\pi x)\\cos(3\\pi x)$."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"metadata": {},
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"outputs": [],
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"source": [
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"def helmholtz_equation(input_, output_):\n",
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" x = input_.extract(\"x\")\n",
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" u_xx = laplacian(output_, input_, components=[\"u\"], d=[\"x\"])\n",
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" f = (\n",
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" -6.0\n",
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" * torch.pi**2\n",
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" * torch.sin(3 * torch.pi * x)\n",
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" * torch.cos(torch.pi * x)\n",
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" )\n",
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" lambda_ = -10.0 * torch.pi**2\n",
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" return u_xx - lambda_ * output_ - f\n",
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"\n",
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"\n",
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"class Helmholtz(SpatialProblem):\n",
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" output_variables = [\"u\"]\n",
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" spatial_domain = CartesianDomain({\"x\": [0, 2]})\n",
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"\n",
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" # here we write the problem conditions\n",
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" conditions = {\n",
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" \"phys_cond\": Condition(\n",
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" domain=spatial_domain, equation=Equation(helmholtz_equation)\n",
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" ),\n",
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" }\n",
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"\n",
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" def solution(self, pts):\n",
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" return torch.sin(torch.pi * pts) * torch.cos(3.0 * torch.pi * pts)\n",
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"\n",
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"\n",
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"problem = Helmholtz()\n",
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"\n",
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"# let's discretise the domain\n",
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"problem.discretise_domain(200, \"grid\", domains=[\"phys_cond\"])"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"As usual, the Helmholtz problem is written in **PINA** code as a class. \n",
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"The equations are written as `conditions` that should be satisfied in the\n",
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"corresponding domains. The `solution`\n",
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"is the exact solution which will be compared with the predicted one. We used\n",
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"Latin Hypercube Sampling for choosing the collocation points."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Solving the problem with a Periodic Network"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Any $\\mathcal{C}^{\\infty}$ periodic function\n",
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"$u : \\mathbb{R} \\rightarrow \\mathbb{R}$ with period\n",
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"$L\\in\\mathbb{N}$ can be constructed by composition of an\n",
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"arbitrary smooth function $f : \\mathbb{R}^n \\rightarrow \\mathbb{R}$ and a\n",
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"given smooth periodic function $v : \\mathbb{R} \\rightarrow \\mathbb{R}^n$ with\n",
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"period $L$, that is $u(x) = f(v(x))$. The formulation is generalizable for\n",
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"arbitrary dimension, see [*A method for representing periodic functions and\n",
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"enforcing exactly periodic boundary conditions with\n",
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"deep neural networks*](https://arxiv.org/pdf/2007.07442).\n",
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"\n",
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"In our case, we rewrite\n",
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"$v(x) = \\left[1, \\cos\\left(\\frac{2\\pi}{L} x\\right),\n",
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"\\sin\\left(\\frac{2\\pi}{L} x\\right)\\right]$, i.e\n",
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"the coordinates augmentation, and $f(\\cdot) = NN_{\\theta}(\\cdot)$ i.e. a neural\n",
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"network. The resulting neural network obtained by composing $f$ with $v$ gives\n",
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"the PINN approximate solution, that is\n",
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"$u(x) \\approx u_{\\theta}(x)=NN_{\\theta}(v(x))$.\n",
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"\n",
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"In **PINA** this translates in using the `PeriodicBoundaryEmbedding` layer for $v$, and any\n",
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"`pina.model` for $NN_{\\theta}$. Let's see it in action! \n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"metadata": {},
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"outputs": [],
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"source": [
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"# we encapsulate all modules in a torch.nn.Sequential container\n",
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"model = torch.nn.Sequential(\n",
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" PeriodicBoundaryEmbedding(input_dimension=1, periods=2),\n",
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" FeedForward(\n",
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" input_dimensions=3, # output of PeriodicBoundaryEmbedding = 3 * input_dimension\n",
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" output_dimensions=1,\n",
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" layers=[10, 10],\n",
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" ),\n",
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")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"As simple as that! Notice that in higher dimension you can specify different periods\n",
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"for all dimensions using a dictionary, e.g. `periods={'x':2, 'y':3, ...}`\n",
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"would indicate a periodicity of $2$ in $x$, $3$ in $y$, and so on...\n",
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"\n",
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"We will now solve the problem as usually with the `PINN` and `Trainer` class, then we will look at the losses using the `MetricTracker` callback from `pina.callback`."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"GPU available: True (mps), used: False\n",
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"TPU available: False, using: 0 TPU cores\n",
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"HPU available: False, using: 0 HPUs\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Epoch 4999: 100%|██████████| 1/1 [00:00<00:00, 154.88it/s, v_num=1, phys_cond_loss=0.033, train_loss=0.033] "
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"`Trainer.fit` stopped: `max_epochs=5000` reached.\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Epoch 4999: 100%|██████████| 1/1 [00:00<00:00, 104.00it/s, v_num=1, phys_cond_loss=0.033, train_loss=0.033]\n"
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]
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}
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],
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"source": [
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"pinn = PINN(\n",
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" problem=problem,\n",
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" model=model,\n",
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")\n",
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"trainer = Trainer(\n",
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" pinn,\n",
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" max_epochs=5000,\n",
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" accelerator=\"cpu\",\n",
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" enable_model_summary=False,\n",
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" callbacks=[MetricTracker()],\n",
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" train_size=1.0,\n",
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" val_size=0.0,\n",
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" test_size=0.0,\n",
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")\n",
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"trainer.train()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# plot loss\n",
|
||
"trainer_metrics = trainer.callbacks[0].metrics\n",
|
||
"plt.plot(\n",
|
||
" range(len(trainer_metrics[\"train_loss\"])), trainer_metrics[\"train_loss\"]\n",
|
||
")\n",
|
||
"# plotting\n",
|
||
"plt.xlabel(\"epoch\")\n",
|
||
"plt.ylabel(\"loss\")\n",
|
||
"plt.yscale(\"log\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We are going to plot the solution now!"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 19,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"<matplotlib.legend.Legend at 0x319b53430>"
|
||
]
|
||
},
|
||
"execution_count": 19,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"pts = pinn.problem.spatial_domain.sample(256, \"grid\", variables=\"x\")\n",
|
||
"predicted_output = pinn.forward(pts).extract(\"u\").tensor.detach()\n",
|
||
"true_output = pinn.problem.solution(pts)\n",
|
||
"plt.plot(pts.extract([\"x\"]), predicted_output, label=\"Neural Network solution\")\n",
|
||
"plt.plot(pts.extract([\"x\"]), true_output, label=\"True solution\")\n",
|
||
"plt.legend()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Great, they overlap perfectly! This seems a good result, considering the simple neural network used to some this (complex) problem. We will now test the neural network on the domain $[-4, 4]$ without retraining. In principle the periodicity should be present since the $v$ function ensures the periodicity in $(-\\infty, \\infty)$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 20,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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|
||
"text/plain": [
|
||
"<Figure size 1500x500 with 3 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# plotting solution\n",
|
||
"with torch.no_grad():\n",
|
||
" # Notice here we put [-4, 4]!!!\n",
|
||
" new_domain = CartesianDomain({\"x\": [0, 4]})\n",
|
||
" x = new_domain.sample(1000, mode=\"grid\")\n",
|
||
" fig, axes = plt.subplots(1, 3, figsize=(15, 5))\n",
|
||
" # Plot 1\n",
|
||
" axes[0].plot(x, problem.solution(x), label=r\"$u(x)$\", color=\"blue\")\n",
|
||
" axes[0].set_title(r\"True solution $u(x)$\")\n",
|
||
" axes[0].legend(loc=\"upper right\")\n",
|
||
" # Plot 2\n",
|
||
" axes[1].plot(x, pinn(x), label=r\"$u_{\\theta}(x)$\", color=\"green\")\n",
|
||
" axes[1].set_title(r\"PINN solution $u_{\\theta}(x)$\")\n",
|
||
" axes[1].legend(loc=\"upper right\")\n",
|
||
" # Plot 3\n",
|
||
" diff = torch.abs(problem.solution(x) - pinn(x))\n",
|
||
" axes[2].plot(x, diff, label=r\"$|u(x) - u_{\\theta}(x)|$\", color=\"red\")\n",
|
||
" axes[2].set_title(r\"Absolute difference $|u(x) - u_{\\theta}(x)|$\")\n",
|
||
" axes[2].legend(loc=\"upper right\")\n",
|
||
" # Adjust layout\n",
|
||
" plt.tight_layout()\n",
|
||
" # Show the plots\n",
|
||
" plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"It is pretty clear that the network is periodic, with also the error following a periodic pattern. Obviously a longer training and a more expressive neural network could improve the results!\n",
|
||
"\n",
|
||
"## What's next?\n",
|
||
"\n",
|
||
"Congratulations on completing the one dimensional Helmholtz tutorial of **PINA**! There are multiple directions you can go now:\n",
|
||
"\n",
|
||
"1. Train the network for longer or with different layer sizes and assert the finaly accuracy\n",
|
||
"\n",
|
||
"2. Apply the `PeriodicBoundaryEmbedding` layer for a time-dependent problem (see reference in the documentation)\n",
|
||
"\n",
|
||
"3. Exploit extrafeature training ?\n",
|
||
"\n",
|
||
"4. Many more..."
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "pina",
|
||
"language": "python",
|
||
"name": "python3"
|
||
},
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.9.21"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 2
|
||
}
|